Electrometers employ circuits which measure current over a wide range and at extremely low levels. For example, mass spectrometers employ current sensors having eight decades of coverage ranging from less than 0.1 pA to 10.0 .mu.A. Feedback amplifiers are commonly employed to convert the sensed current measurement to a voltage measurement. The voltage is applied to an analog to digital (A/D) converter, the output of which is processed by a computer to generate a desired output.
The most straightforward means for measuring current is an operational amplifier (hereinafter "op-amp") feedback configuration which employs a resistor R as a feedback element as shown in FIG. 1A. The operational amplifier 30 includes a negative feedback terminal 32A, a positive feedback terminal 32B, and an output terminal 34. Resistor R is coupled across the output terminal 34 and negative feedback terminal 32A, thereby providing a feedback loop. The positive feedback terminal 32B is grounded as shown. In this manner, the output voltage V.sub.o is related to the input current I.sub.in according to the following relationship: EQU V.sub.o =I.sub.in R. (1)
Such a configuration requires a large resistor R for measurement of small levels of current; however large resistors are a source for thermal noise. In addition, stray capacitance inherent in the op-amp 40 and resistor R in conjunction with a high value resistor R can lead to an impractically-large time constant.
The dynamic range of such a configuration is limited by the use of a single resistor R. When large current values are to be measured, a small value resistor R is required or else the voltage at the output V.sub.o will saturate, i.e., V.sub.o will match the source voltage levels applied to the op-amp 30. A resistor bank including resistors R.sub.a, R.sub.b, R.sub.c and physical switches S.sub.a, S.sub.b, S.sub.c provides selectable resistance levels. Such a configuration is undesirable, as switches with minimal leakage current are sophisticated and therefore expensive. A further limitation of this configuration is that it requires a high-resolution analog-to-digital converter 56 to obtain accurate low-level current measurements, in the case where few resistors are used in the resistor bank.
An integrator amplifier as shown in Prior Art FIG. 1B employs a capacitor C as the feedback element. This circuit integrates the input signal I.sub.in to provide an output voltage V.sub.o. In this embodiment, the relationship is characterized as: ##EQU1## As capacitor C charges, the voltage across the capacitor ramps upward or downward, depending on the direction of the applied current I.sub.in. The slope of the ramp dV.sub.o /dt varies with the level of applied input current I.sub.in. The output voltage V.sub.o is measured for a predetermined time interval to provide the degree of the slope, and a corresponding input current I.sub.in is determined based on that value. A reset switch S periodically discharges the capacitor C to prevent saturation of the output voltage V.sub.o.
The integrator embodiment mitigates the thermal noise problem; however it suffers from several limitations. A small capacitor C is required for small current measurement; for example, if measurements on the order of 1 pA are required, a small capacitor C, for example a 1 pA capacitor, is employed. Such a small capacitance is nearly equal to the parasitic capacitance of the op-amp 30, which varies with the input signal and is sensitive to temperature. This embodiment is further limited by leakage current through the op-amp when the switch S is open. To achieve wide-dynamic range, a bank of capacitors are required, and therefore a switch is required to select a capacitance level. This introduces the imitations described above in the FIG. 1A embodiment. The primary limitation of this embodiment lies in that field effect transistors (FETs) are commonly used for the reset switch S, which tends to introduce further leakage current, adversely affecting signal measurements.
A logarithmic amplifier, as shown in Prior Art FIG. 1C employs a diode D as the feedback element for the op-amp 30. The transfer function for this embodiment is given by: ##EQU2## where k is the Boltzman time constant, T is temperature in Kelvin, q is the electron charge, I.sub.in is the input current, and I.sub.s is the reverse saturation current (diode-dependent, usually on the order of 10.sup.-15 A). A second diode D.sub.1 is included to allow for bipolar transmission.
The logarithmic amplifier embodiment takes advantage of the logarithmic relationship between output voltage V.sub.o and input current I.sub.in introduced by the diodes D.sub.1, D.sub.2, to offer a significant improvement in dynamic range over the aforementioned embodiments. However, it suffers from the limitation of extreme temperature sensitivity, due to the dependence of the transfer function on T, but especially due to the exponential temperature-dependency of the reverse saturation current factor I.sub.s. For example, the temperature coefficient causes an output voltage V.sub.o variance at a rate of approximately -2.1 mV/.degree.C. near room temperature. This results in a decade variance in V.sub.o when the operating temperature changes by 30.degree. C.
To avoid this problem, some have employed a differential log measurement to cancel the temperature dependency of I.sub.s, which provides a certain level of improvement. The temperature of the circuit can be stabilized; however, this is an expensive solution, which proves to be impractical for many applications.
As illustrated in the schematic diagram of Prior Art FIG. 1D, others have employed a calibration technique which periodically provides a known reference current I.sub.ref to the amplifier 30, and measures the resulting output voltage V.sub.o. By taking data over a range of reference current levels I.sub.ref, a calibration chart can be generated and used to correct sensor measurements; thus, rendering the amplifier insensitive to temperature.
To generate the known reference current values I.sub.ref, a switchable resistor bank 31, including resistors R.sub.A, R.sub.B, R.sub.N, and corresponding switches S.sub.A, S.sub.B, S.sub.N, has been employed in combination with a reference voltage source V.sub.ref. Such a configuration introduces leakage current at the switches S.sub.A, S.sub.B, S.sub.N, and, more significantly, generates a large reference current I.sub.ref error due to DC offset error at the op-amp 30, which can lead to excessive error when measuring low current levels. For example, when introducing reference current I.sub.ref levels on the order of 1 pA, to generate the 1 pA reference current, a 1 G.OMEGA. resistor is required assuming an input voltage of 1 mV. Assuming a DC offset in the op-amp 30 of 1 mV (a common DC offset error in electrometer grade op-amps), this would lead to an error factor of 100 percent. Therefore, in this configuration, when the offset error of the op-amp 30 approaches the input voltage V.sub.ref, the resultant error in the input current I.sub.ref is significant, limiting performance of the circuit.